There exist a number of posts related to this issue in this site, for example:
What's behind Method -> {"EquationSimplification" -> "Residual"}
Why does NDSolve need to solve for the derivatives if the equations are already explicitly solved?
Introduction to Vectors and NDSolve with System of Equations
Plot with different colors the results of an NDSolve with vector solution
Numerically solve large ODE system
System of ODEs specified by large coefficient matrices
There should be more. In short, large symbolic ODE system is burdensome, it's better to vectorize the system or make small black-box function if possible. In your case, the system can be transformed to the following form:
$$U'(t)=m_0+m_1.U(t)+m_2.U(t).U(t)$$
According to your statement here, I guess you already have $m_0$ etc. at hand, so it should be easy for you to build such a equation, but here I'll rebuild this equation from the code given by you with the help of powerful CoefficientArrays
:
{ode, ic} = Uncompress@"1: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";
{m0, m1, m2} =
CoefficientArrays[Last /@ ode,
Through[{rZ, rY, rA, rB, rC, rD, rE, rF, rG, rH, rI, rJ, rK, rL, rM, rN, rO, rP, rQ,
rR, rS, rT, ra, rb, rc, rd, re, rf, rg, rh, ri, rj, rk, rl, rm, rn, ro, rp, rq,
rr, rs, rt}[t$111993]]];
icvalue = Last /@ ic;
Clear@rhs; rhs[var_?VectorQ] := m0 + m1.var + m2.var.var
sol = NDSolveValue[{var'[t] == rhs@var[t], var[0] == icvalue},
var, {t, 0, 10^4}]; // AbsoluteTiming
(* {0.917296, Null} *)
sol // ListLinePlot

MatrixExp[]
. If it's nonlinear... good luck, dude. $\endgroup$